Chapter 48 Red Black Trees

Objectives To know what a red-black tree is (§48.1). To convert a red-black tree to a 2-4 tree and vice versa (§48.2). To design the RBTree class that extends the BinaryTree class (§48.3). To insert an element in a red-black tree and resolve the double red problem if necessary (§48.4). To insert an element from a red-black tree and resolve the double black problem if necessary (§48.5). To implement and test the RBTree class (§§48.6-48.7). To compare the performance of AVL trees, 2-4 trees, and RBTree (§48.8).

What is a Red Black Tree? A red-black tree is a binary search tree, which is derived from a 2-4 tree. A red-black tree corresponds to a 2-4 tree. Each node in a red-black tree has a color attribute red or black.

What is a Red Black Tree? A node is called external if its left or right subtree is empty. Note that a leaf node is external, but an external node is not necessarily a leaf node. For example, node 25 is external, but it is not a leaf. The black depth of a node is defined as the number of black nodes in a path from the node to the root. For example, the black depth of node 25 is 2 and the black depth of node 27 is 2.

Properties A red-black tree has the following properties: The root is black. Two adjacent nodes cannot be both red. All external nodes have the same black depth.

Conversion between Red-Black Trees and 2-4 Trees To convert a red-black tree to a 2-4 tree, simply merge any red nodes with its parent to create a 3-node or a 4-node. To convert a 2-4 tree to a red-black tree, perform the transformations for each node :

Conversion not unique the conversion from a 2-4 tree to a red-black tree is not unique.

2-4 Tree Animation http://www.cs.armstrong.edu/liang/animation/RBTreeAnimation.html

Designing Classes for Red Black Trees RBTree TestRBTree Run